Pulmonary vein isolation gap finder

ABSTRACT

A gap between a plurality of ablation sites in a heart that hinders electrical propagation therethrough is found by projecting the locations of the sites in a 3-dimensional coordinate system onto a simulation plane, identifying a set of shortest 3-dimensional paths that correspond to 2-dimensional connections between pairs of the projected locations of the sites, and reporting a gap as a longest one of the set.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Application claims the benefit of U.S. Provisional Application No.62/252,109, filed 6 Nov. 2015, which is herein incorporated byreference.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialthat is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightrights whatsoever.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to medical instrumentation for tissue ablation.More particularly, this invention relates to treating cardiacarrhythmias by ablating in a vicinity of pulmonary venous tissue.

2. Description of the Related Art

It is now well-known that atrial fibrillation can be triggered byaberrant conduction pathways that originate in muscle bundles thatextend from the atrium to the pulmonary veins and that ablation in orderto produce electrical pulmonary vein isolation ablation can maintainsinus rhythm.

Contact force methods are effective in accomplishing circumferentialpulmonary vein isolation. For example, commonly assigned U.S. Pat. No.6,997,924 to Schwartz et al, which is herein incorporated by reference,describes pulmonary vein isolation using high energy emission of laserlight energy. After transseptal advancement of a catheter to the ostiumof a pulmonary vein, an anchoring balloon is expanded to position amirror near the ostium of the pulmonary vein, such that light energy isreflected and directed circumferentially around the ostium of thepulmonary vein when a laser light source is energized. A circumferentialablation lesion is thereby produced, which effectively blocks electricalpropagation between the pulmonary vein and the left atrium.

More recently hybrid catheters having contact force sensors and locationsensors have been employed to isolate the pulmonary veins electrically,such as the Smart Touch™ catheter. However, residual conduction gaps mayremain in some patients despite optimal ablation.

SUMMARY OF THE INVENTION

There is provided according to embodiments of the invention a method,which is carried out by ablating a plurality of sites in a heart of aliving subject, projecting the locations of the sites in a 3-dimensionalcoordinate system onto a simulation plane, identifying a set of shortest3-dimensional paths that correspond to 2-dimensional connections betweenpairs of the projected locations of the sites, and reporting a gap as alongest one of the set.

Yet another aspect of the method which is carried out by defining asource and a destination, projecting the source and the destination ontothe simulation plane. The projected locations of the sites lie betweenthe projected source and the projected destination on the simulationplane. The method is further carried out by randomly generating2-dimensional paths on the simulation plane extending from the projectedsource to the projected destination, with passages between two of theprojected locations of sites. The method is further carried out bydetermining a minimum size of the passages for each of the 2-dimensionalpaths, and reporting the largest minimum size of the 2-dimensionalpaths.

In still another aspect of the method the projected locations of thesites lie on an ellipse of best fit, wherein a portion of the projectedlocations of the sites lie outside the ellipse. The method is furthercarried out by enlarging the ellipse to include all of the projectedlocations of the sites.

An additional aspect of the method is carried out by modeling a portionof the heart as a triangular mesh including ablation points, and fromthe mesh nodes preparing a grid graph of graph nodes that are connectedby undirected edges, representing the ablation points on the grid graphas corresponding graph nodes of the nearest mesh node thereof, and usingthe corresponding graph nodes as the projected locations of the sites togenerate 2-dimensional paths.

There is further provided according to embodiments of the invention amethod, which is carried out by ablating a plurality of sites in a heartof a living subject, and building a tree graph from all of the3-dimensional locations of the sites. The method is further carried outby defining a path constructed of shortest segments between pairs of thesites, selecting a source, wherein the tree graph has a loop that windsabout the source, the loop describing a gap between two of the ablationsites. The method is further carried out by reporting a shortest edge inthe tree graph that can close the gap.

Another aspect of the method includes selecting additional sources anditerating the step of building a tree graph using the additionalsources.

There is further provided according to embodiments of the invention anapparatus, including a probe adapted for insertion into contact with aheart in a body of a subject. The probe has a location sensor and anelectrode on a distal portion of the probe, an ablation power generator,a processor linked to the location sensor, and arranged cooperativelywith the ablation power generator for ablating a plurality of sites inthe heart. The processor is operative for projecting the locations ofthe sites onto a simulation plane, identifying a set of shortest3-dimensional paths that correspond to 2-dimensional connections betweenpairs of the projected locations of the sites, and reporting a gap as alongest one of the 3-dimensional paths.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

For a better understanding of the present invention, reference is madeto the detailed description of the invention, by way of example, whichis to be read in conjunction with the following drawings, wherein likeelements are given like reference numerals, and wherein:

FIG. 1 is a pictorial illustration of a system for performingcatheterization procedures on a heart, in accordance with a disclosedembodiment of the invention;

FIG. 2 is a flow chart of a method of determining a gap in an ablatedregion of tissue, in accordance with an embodiment of the invention;

FIG. 3 is a graphical illustration of an aspect of the method describedin FIG. 2 in accordance with an embodiment of the invention;

FIG. 4 is a flow chart of a method of establishing the source anddestination of a path in accordance with an embodiment of the invention;

FIG. 5 is a flow chart of a method of establishing the source anddestination of a path in accordance with an alternate embodiment of theinvention;

FIG. 6 is a flow chart of a method of path generation in accordance withan embodiment of the invention;

FIG. 7 is a flow chart of a method of determining a gap in an ablatedregion of tissue in accordance with an alternate embodiment of theinvention;

FIG. 8 illustrates a weighted graph prepared from a 3-dimensional meshin accordance with an embodiment of the invention;

FIG. 9 is a detailed flow chart of an aspect of the method shown in FIG.7 in accordance with an embodiment of the invention;

FIG. 10 is a detailed flow chart of an aspect of the method shown inFIG. 7 in accordance with an alternate embodiment of the invention;

FIG. 11 is a flow chart detailing generation of a path according to themethod shown in FIG. 7 in accordance with an embodiment of theinvention;

FIG. 12 is an exemplary graph of ablation sites in accordance with anembodiment of the invention;

FIG. 13 is a flow chart of a method of path generation in accordancewith an embodiment of the invention;

FIG. 14 is a graph illustrating an aspect of the method shown in FIG. 13in accordance with an embodiment of the invention;

FIG. 15 is a graph illustrating another aspect of the method shown inFIG. 13 in accordance with an embodiment of the invention;

FIG. 16 is a tree graph resulting from the performance of a step themethod shown in FIG. 13 in accordance with an embodiment of theinvention;

FIG. 17 is a 3-dimensional presentation of the points corresponding ofthe tree graph of FIG. 16 in accordance with an embodiment of theinvention;

FIG. 18 is an exemplary loop graph that is evaluated in the method shownin FIG. 13, in accordance with an embodiment of the invention;

FIG. 19 is a composite screen display that was produced in accordancewith an embodiment of the invention; and

FIG. 20 is a screen display illustrating multiple gaps found in acollection of ablation points in accordance with an embodiment of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, numerous specific details are set forth inorder to provide a thorough understanding of the various principles ofthe present invention. It will be apparent to one skilled in the art,however, that not all these details are necessarily needed forpracticing the present invention. In this instance, well-known circuits,control logic, and the details of computer program instructions forconventional algorithms and processes have not been shown in detail inorder not to obscure the general concepts unnecessarily.

Documents incorporated by reference herein are to be considered anintegral part of the application except that, to the extent that anyterms are defined in these incorporated documents in a manner thatconflicts with definitions made explicitly or implicitly in the presentspecification, only the definitions in the present specification shouldbe considered.

Definitions.

Discrete contour: a set of geodesic segments in a curved 2-dimensionalspace that form a closed curve.

Contour gap: the longest segment in a discrete contour.

Contour vertices: spheres between a pair of segments. The spheres canhave finite radii.

Segment length: the Euclidean or geodesic distance between the vertices'centers minus the vertices' radii.

Isolation: a surface that prevents current flow from a source to adestination. If the current propagates in 2-dimensional space (e.g., aplane or the tissue of an atria) then isolation is a contour. Ifmultiple possible surfaces exist, an isolating test should be definedfor comparison. If the hindrance of the current flow through a slit,i.e., a gap between two vertices, decreases with the gap width, anisolating test could be constructed so that the discrete contour withthe smallest gap becomes the isolation.

Winding number of a closed curve: the number of times a closed curve ina 2-dimensional curved space, winds about a predefined point source.

Current flow path: an open curve from a current source to a currentdestination.

Path contour segment intersection: a point where a closed contourintersects a current flow path.

System Overview.

Turning now to the drawings, reference is initially made to FIG. 1,which is a pictorial illustration of a system 10 for evaluatingelectrical activity and performing ablative procedures on a heart 12 ofa living subject, which is constructed and operative in accordance witha disclosed embodiment of the invention. The system comprises a catheter14, which is percutaneously inserted by an operator 16 through thepatient's vascular system into a chamber or vascular structure of theheart 12. The operator 16, who is typically a physician, brings thecatheter's distal tip 18 into contact with the heart wall, for example,at an ablation target site. Electrical activation maps may be prepared,according to the methods disclosed in U.S. Pat. Nos. 6,226,542, and6,301,496, and in commonly assigned U.S. Pat. No. 6,892,091, whosedisclosures are herein incorporated by reference. One commercial productembodying elements of the system 10 is available as the CARTO® 3 System,available from Biosense Webster, Inc., 3333 Diamond Canyon Road, DiamondBar, Calif. 91765. This system may be modified by those skilled in theart to embody the principles of the invention described herein.

Areas determined to be abnormal, for example by evaluation of theelectrical activation maps, can be ablated by application of thermalenergy, e.g., by passage of radiofrequency electrical current throughwires in the catheter to one or more electrodes at the distal tip 18,which apply the radiofrequency energy to the myocardium. The energy isabsorbed in the tissue, heating it to a point (typically about 60° C.)at which it permanently loses its electrical excitability. Whensuccessful, this procedure creates non-conducting lesions in the cardiactissue, which disrupt the abnormal electrical pathway causing thearrhythmia. The principles of the invention can be applied to differentheart chambers to diagnose and treat many different cardiac arrhythmias.

The catheter 14 typically comprises a handle 20, having suitablecontrols on the handle to enable the operator 16 to steer, position andorient the distal end of the catheter as desired for the ablation. Toaid the operator 16, the distal portion of the catheter 14 typicallycontains at least one position sensor 21 that provide signals to aprocessor 22, located in a console 24. The position sensors 21 may be amagnetic sensor or an electrode for an impedance-based locating system,as taught in U.S. Pat. No. 7,536,218, issued to Govari et al., which isherein incorporated by reference. The processor 22 may fulfill severalprocessing functions as described below.

Ablation energy and electrical signals can be conveyed to and from theheart 12 through one or more ablation electrodes 32 located at or nearthe distal tip 18 via cable 34 to the console 24. Pacing signals andother control signals may be conveyed from the console 24 through thecable 34 and the electrodes 32 to the heart 12. Sensing electrodes 33,also connected to the console 24 are disposed between the ablationelectrodes 32 and have connections to the cable 34.

Wire connections 35 link the console 24 with body surface electrodes 30and other components of a positioning sub-system for measuring locationand orientation coordinates of the catheter 14. The processor 22 oranother processor (not shown) may be an element of the positioningsubsystem. The electrodes 32 and the body surface electrodes 30 may beused to measure tissue impedance at the ablation site as taught in U.S.Pat. No. 7,536,218, issued to Govari et al., which is hereinincorporated by reference. A temperature sensor (not shown), typically athermocouple or thermistor, may be mounted on or near each of theelectrodes 32.

The console 24 typically contains one or more ablation power generators25. The catheter 14 may be adapted to conduct ablative energy to theheart using any known ablation technique, e.g., radiofrequency energy,ultrasound energy, and laser-produced light energy. Such methods aredisclosed in commonly assigned U.S. Pat. Nos. 6,814,733, 6,997,924, and7,156,816, which are herein incorporated by reference.

In one embodiment, the positioning subsystem comprises a magneticposition tracking arrangement that determines the position andorientation of the catheter 14 by generating magnetic fields in apredefined working volume and sensing these fields at the catheter,using field generating coils 28. The positioning subsystem is describedin U.S. Pat. No. 7,756,576, which is hereby incorporated by reference,and in the above-noted U.S. Pat. No. 7,536,218.

As noted above, the catheter 14 is coupled to the console 24, whichenables the operator 16 to observe and regulate the functions of thecatheter 14. Console 24 includes a processor, preferably a computer withappropriate signal processing circuits. The processor is coupled todrive a monitor 29. The signal processing circuits typically receive,amplify, filter and digitize signals from the catheter 14, includingsignals generated by sensors such as electrical, temperature and contactforce sensors, and a plurality of location sensing electrodes (notshown) located distally in the catheter 14. The digitized signals arereceived and used by the console 24 and the positioning system tocompute the position and orientation of the catheter 14, and to analyzethe electrical signals from the electrodes.

In order to generate electroanatomic maps, the processor 22 typicallycomprises an electroanatomic map generator, an image registrationprogram, an image or data analysis program and a graphical userinterface configured to present graphical information on the monitor 29.

Typically, the system 10 includes other elements, which are not shown inthe figures for the sake of simplicity. For example, the system 10 mayinclude an electrocardiogram (ECG) monitor, coupled to receive signalsfrom one or more body surface electrodes, in order to provide an ECGsynchronization signal to the console 24. As mentioned above, the system10 typically also includes a reference position sensor, either on anexternally-applied reference patch attached to the exterior of thesubject's body, or on an internally-placed catheter, which is insertedinto the heart 12 maintained in a fixed position relative to the heart12. Conventional pumps and lines for circulating liquids through thecatheter 14 for cooling the ablation site are provided. The system 10may receive image data from an external imaging modality, such as an MRIunit or the like and includes image processors that can be incorporatedin or invoked by the processor 22 for generating and displaying images.

It is desired that the lesions produced by the applications form acontinuous line, so as to block electrical propagation thereacross. Theprocedures described below analyze the relationships among the lesionsto determine whether significant gaps in the line exist. It should benoted that ablations sites exist in 3-dimensional space, but thepresentation on a display represents a projection of three dimensionsonto another surface, typically a 2-dimensional plane. Human evaluationof the display is possible, for example by repeated inspection usingimage rotation techniques, but is tedious and error-prone because ofsuperposition of the spheres, e.g., a gap could be missed by the humanoperator, which could result in recurrence of the arrhythmia or evencomplete failure of the procedure. Operator-performance of this taskinvariably increases the duration of the catheterization session andhence the risk to the patient, and furthermore may limit the number ofpatients who can be evaluated in the catheterization laboratory

One method of recording information concerning ablation sites is theVisiTag™ module, which is a component of the above-noted CARTO system.

The following summarizes two methods of finding the isolation, which arepresented in detail in the embodiments below.

First Method.

-   -   (a) Generate all possible current flow paths. Since this isn't        really possible, randomly generate a very large number of paths        that can simulate the entire flow.    -   (b) For each path, find all intersecting segments and select the        segment with the smallest segment length. Add these segments to        a list of candidates.    -   (c) The segment with the largest segment length in the list is        the largest gap in the isolation.    -   (d) The rest of the isolation curve can be found by elimination        of curves that do not have the largest gap and trimming the list        accordingly.

Second Method.

-   -   (a). Find the discrete contour constructed from the smallest        segments that winds around a source only once.

First Embodiment

“No Map File” Variant.

Since an electric wave travels on the tissue surface, the wave'spropagation and percolation can be simulated as a randomly propagating1-dimensional wavefront. The simulation involves a random generation ofmultiple paths from the suspected source (the pulmonary veins) to thedestination. The destination is a point on a closed contour comprisingthe tissue surface, and is beyond all sites of ablation. In other words,the line of ablation lies between the source and the destination. Eachpath comprises a series of steps from one intermediate point to the nextuntil the destination is reached.

This variant does not rely on the existence of a map file describing thegeometry of the atria.

Beginning at the source, the length and direction of each step of a pathare randomly generated until the path reaches the destination.Propagation along such a path is treated as being hindered by thesmallest gap between ablation sites in the path. The width of this gapis stored as the “blocking value” of the path.

If enough paths are generated, all plausible gaps will be traversed andmapped. The largest blocking value among the paths is reported as thesize of the gap.

Each ablation site corresponds to a record in a database, for example,the above-noted VisiTag module. A variety of data is contained in eachrecord, including the 3-dimensional coordinates of the site, contactforce, duration of power application, and other information not relevantto this disclosure.

The procedure described below is particularly efficient if a source anddestination of the paths to be generated are provided by the operator.However, as explained below in the discussion of FIG. 5, it is possibleto estimate the source and destination automatically at some cost inaccuracy. In cases where ablation dimensions are provided, they can beaccounted for in the gap calculations.

Reference is now made to FIG. 2, which is a flow chart of a method ofdetermining a gap in an ablated region of tissue, in accordance with anembodiment of the invention. The process steps are shown in a particularlinear sequence in this and other flowcharts herein for clarity ofpresentation. However, it will be evident that many of them can beperformed in parallel, asynchronously, or in different orders. Thoseskilled in the art will also appreciate that a process couldalternatively be represented as a number of interrelated states orevents, e.g., in a state diagram. Moreover, not all illustrated processsteps may be required to implement the method. The method is describedin reference to the example of pulmonary vein isolation; however it isapplicable to other ablation procedures in the heart.

At initial step 37 the subject is catheterized, and a series ofablations at respective sites is performed, typically, the ablationseffect isolation of a pulmonary vein (PVI). Data relevant to eachablation site is memorized as noted above. The operator may be presentedwith a display illustrating the sites and data pertaining to theablations.

Next, at step 39 the Euler distances between all pairs of ablation sitesare calculated. It will be recalled that the 3-dimensional coordinatesof the sites can be determined using the position sensor 21 (FIG. 1).Alternatively, the radii of the lesions created at the sites may bepredicted using known methods and taken into consideration for thedistance computation. This of course reduces the effective distancesbetween the pair.

Next, at step 41 the source and destination for the paths areestablished. The paths are projected onto a canonical ellipse, whoseparameters are obtained in variants of step 41, which are describedbelow. The plane of the ellipse is referred to herein as a “simulationplane”.

Next, at step 43, using the 3-dimensional spatial coordinates of theablation sites, the points of ablation are transformed onto thesimulation plane. Reference is now made to FIG. 3, which is a graphicalillustration of the procedure described in step 43 in accordance with anembodiment of the invention. A subset of ablation points 45 isillustrated for simplicity. The 2-dimensional projection of the ablationpoints 45 appears as a series of transformed ablation points 51 that liewithin the bounds of an ellipse 53. Source 55 and destination 57 areindicated. Sites of energy application, typically radiofrequency energy,are represented by three color-coded categories of the ablation points45, as indicated by different hatched patterns. While three categoriesare indicated on FIG. 3 for convenience of presentation, many gradationsmay be color-coded and presented on a suitable display monitor. Thegradations may indicate levels of power intensity. From this and othermemorized information concerning the ablation site, such as duration ofpower application, and contact force, it is possible to predict thediameter of the lesions created, for example from the teachings ofcommonly assigned U.S. Patent Application Publication No. 20140100563 byGovari et al., which is herein incorporated by reference.

At step 59 (FIG. 2) the points 51 are chosen pairwise, and line segmentsdefined by each pair are mapped. For example, the pairs 61, 63, 65 mapto line segments 67, 69, 71, respectively, The lengths of the linesegments 67, 69, 71 reflect the Euler distances between the pairs 61,63, 65.

Reverting to FIG. 2, at step 73 a maximum step size (stepMax) isdetermined. This may be calculated by dividing the longest distancebetween ablation sites by a user-configured value, e.g., 20. This valueaffects convergence of the simulation.

Next, at step 75 a path is generated, as described below. Step 75 isperformed iteratively. Associated with each path created by aperformance of step 75 is a minimum blocking value, i.e., the Eulerdistance of a line segment connecting two ablation points and crossed bythe path.

Next, at decision step 77, it is determined if a termination criterionfor the iteration of step 75 has been reached. For example, thecriterion can be a predetermined number of iterations, the expiration ofa time interval, or a combination thereof. If the determination atdecision step 77 is negative, then control returns to step 75.

If the determination at decision step 77 is affirmative, then controlproceeds to final step 79. A gap in the ablation points is reported asthe largest of the minimum block lengths found in the paths generated instep 75.

Reference is now made to FIG. 4, which is a flow chart of one method ofestablishing the source and destination (step 41; FIG. 2) in accordancewith an embodiment of the invention. Parameters of the canonical ellipseare obtained at initial step 81 using the least squares of the distanceresiduals (measured from a site position obtained from the canonicalellipse equations). Alternatively, the parameters may be obtained bytaking the singular value decomposition of all sites, which affects thethree radii of an ellipsoid that can be generated from the canonicalellipse. The two larger radii span a plane. These techniques are knownin the art and are not further discussed herein.

Next, at step 83 a source point for a conduction path is determined byan operator. The source point may be chosen using a graphical userinterface, for example by a mouse click on a screen display.

Next, at step 85 the 2-dimensional projection of the ablation pointclosest to the source point chosen in initial step 81 is identified.Using this point minimizes computation time.

Next, at step 87 a source region is defined on the simulation planeabout the source point as a circle centered on the source point andhaving a radius equal to the distance from the source point to theablation point identified in step 85.

Then, at final step 89, the other ablation points are projected onto thesimulation plane.

Reference is now made to FIG. 5, which is a flow chart of another methodof performing step 41 (FIG. 2), in accordance with an embodiment of theinvention. In this variant the source and destination are estimatedautomatically.

In initial step 91 the ablation sites are fitted into the canonicalellipse, which is established as described above with respect to initialstep 81 (FIG. 4) to define the simulation plane. The ellipse of best fitmay not include all the ablation points, but should include the majorityof them.

Next, at step 93 the ablation points are projected onto the simulationplane.

Next, at step 95, keeping its aspect ratio constant, the ellipse definedand fitted in initial step 91 is enlarged to include all the projectedablation points

Then, at final step 97, the ellipse resulting from step 95 is reportedas the destination for the paths.

Reference is now made to FIG. 6, which is a flow chart detailing pathgeneration (step 75; FIG. 2), in accordance with an embodiment of theinvention. At initial step 99 a suitably limited random number isgenerated. This number represents an angle between from 0 to 360 degreesand designates a point of origin for the path on the contour of thesource, usually a circle or ellipse.

Next, at step 101 a current blocking value is set. This is initializedto the largest real number that can be represented in the processor.

Next, at step 103 a step is created, having with a length (r) anddirection (θ) determined randomly (r˜Uniform[0; stepMax], θ˜Uniform[0;2π]).

Next, at decision step 105, it is determined if on the simulation plane(1) the step crosses a 2-dimensional line segment that connects a pairof projected ablation sites and (2) the 3-dimensional Euler distancebetween that pair is smaller than the current blocking value.

If the determination at decision step 105 is affirmative, then controlproceeds to step 107. The current blocking value is reset to the3-dimensional Euler distance between the pair.

After performing step 107 or if the determination at decision step 105is negative, at decision step 109 it is determined if the path hasintersected the source.

If the determination at decision step 109 is affirmative, then at step111 the path is reflected at an angle (θ_(r)) according to its angle ofincidence (θ_(i)) on the source (θ_(r)=θ_(i)). When the source is apoint, reflection is not required.

After performing step 111 or if the determination at decision step 109is negative, at decision step 113, it is determined if the destinationhas been reached. If the determination is negative, then control returnsto step 103 to create another random step.

If the determination at decision step 113 is affirmative, then theprocedure ends at final step 115.

Map File Variant.

This variant is used when a map file, i.e., a mesh file, exists as a mapof the atria. Such files can be generated, for example, using theteachings of U.S. Patent Application Publication No. 20140125653,entitled Combining Three-Dimensional Surfaces, U.S. Pat. No. 9,265,434,entitled Dynamic Feature Rich Anatomical Reconstruction from a PointCloud and U.S. Patent Application Publication No. 20150018698, entitledModel Based Reconstruction of the Heart from Sparse Samples, all ofwhich are commonly assigned and herein incorporated by reference.Ablation points as shown in FIG. 3 are available for this variant.

Reference is now made to FIG. 7, which is a flow chart of a method ofdetermining a gap in an ablated region of tissue, in accordance with analternate embodiment of the invention. Triangle vertices and indices areretrieved from the mesh file at initial step 117 and used as graphnodes. The graphs produced in this variant are referred to as “gridgraphs”, by which they may be distinguished from “tree graphs” and otherconfigurations discussed elsewhere herein. While the vertices aredefined as a mesh in 3-dimensional space, the nodes are defined in anabstract topological space.

Next, at step 119 a weighted grid graph with nodes and undirected edgesis prepared. The graph is weighted according to the 3-dimensional Eulerdistances between neighboring vertices.

Reference is now made to FIG. 8, which illustrates a weighted grid graph121 prepared according to step 119 (FIG. 7) from a 3-dimensional mesh123, in accordance with an embodiment of the invention. Portions of thegrid graph 121 are referred to as sub-graphs, e.g., sub-graph 125 is asub-graph of grid graph 121. The grid graph 121 comprises bulk nodes,which include nodes of the sub-graph 125 and nodes 127 that are outsidethe sub-graph 125. Sub-graph 125 also comprises sub-graph bulk nodes,which are entirely within the sub-graph 125 and are connected only toother nodes of the sub-graph 125. The grid graph 121 also comprisesnodes 129 that are in contact with surface nodes of the sub-graph 125,e.g., node 131. As will be seen from the discussion below, bulk nodes ofthe source, e.g., sub-graph 125 can be removed to simplify thecalculation and the surface nodes on the boundary, e.g., node 131, canbe used as the first step in a simulated path.

Referring to FIG. 7 and to FIG. 8, ablation points that are modeled onthe mesh 123, e.g., ablation point 126, may lie between nodes of themesh 123. Such ablation points are not projected directly onto the gridgraph 121, but at step 133 are treated as the projections of theirnearest mesh vertices. Thus, a projection of node 128 (the node on themesh 123 closest to the ablation point 126) onto the grid graph 121 ascorresponding graph node 130 would represent ablation point 126 on thegrid graph.

Next, at step 135 a source and a destination are selected by retrievalof the source by the operator. Alternatively the source and destinationmay be estimated. Details of step 135 are provided below.

Next, at step 137 paths on the simulation plane connecting each pair ofprojected ablation sites are identified. The length of the shortest3-dimensional path between each pair of the projected ablation sites isdetermined for the connections. This step constitutes a solution to theshortest path problem. It is accomplished using a known algorithm, e.g.,Dijkstra's algorithm, or several other known algorithms. The standardalgorithm provided in Mathematica® is suitable for step 137.Alternatively, a “breadth-first” scan may be performed.

Next, at step 139 assign to each node a respective “blocking value”. Theblocking value corresponds to the shortest one of the paths developed instep 137 that passes through the node. If none of the paths passesthrough a node, its blocking value is treated as infinite.

Next, at step 141 a path is generated, as described below. Step 141 isperformed iteratively. Associated with each path created by aperformance of step 141 is a minimum blocking value, i.e., the Eulerdistance of a line segment connecting two ablation points and crossed bythe path.

Next, at decision step 143 it is determined if a termination criterionfor the iteration of step 141 has been reached. For example, this can bea predetermined number of iterations, or the expiration of a timeinterval, or a combination thereof. If the determination at decisionstep 143 is negative, then control returns to step 141.

If the determination at decision step 143 is affirmative, then controlproceeds to final step 145. A gap in the ablation points is reported asthe largest of the minimum blocking values found in the paths generatedin the iterations of step 141.

Reference is now made to FIG. 9, which is a detailed flow chart of themethod of step 135 (FIG. 7) in accordance with an embodiment of theinvention. The source and destination of a path are obtained byretrieval from the operator, in accordance with an embodiment of theinvention.

At initial step 147 a source input and destination are chosen by theoperator. Using a graphical user interface, the operator identifies asource point in 3-dimensional space, and draws a 2-dimensional ellipseto define the destination. Next, at step 149 a destination canonicalellipse parameter is obtained as described above, resulting in a2-dimensional ellipse located in 3-dimensional space.

Next, at step 151 nodes of the grid graph prepared in step 119 having3-dimensional coordinates that fall outside the ellipse are removed fromthe graph.

Next, at step 153 the ablation site nearest to the source input chosenin initial step 147 is identified.

Next, at step 155 the source is defined as the 1-dimensional surface ofa sub-graph of the weighted graph generated in step 119 (FIG. 7) withinthe distance from the source input chosen at initial step 147 to thenearest projected ablation site.

Then, at final step 157 all bulk nodes from the weighted grid graphprepared in step 119 (FIG. 7), i.e., the sub-graph bulk nodes of thesub-graph 125 (FIG. 8) are removed from further consideration.

Alternatively, the source and destination can be estimated using amodification of the method described above with respect to FIG. 5.Reference is now made to FIG. 10, which is a detailed flow chart of step135 (FIG. 7) in accordance with an alternate embodiment of theinvention. In this variant the source and destination are estimatedautomatically. Steps 91, 93, 95 are common to the method of FIG. 5 andare not re-described. Then, in step 159 the ellipse is shrunk to excludeall projected ablation points from its borders.

After performing step 159, in final step 161 only nodes from theweighted grid graph prepared in step 119 having 3-dimensionalcoordinates that project between the enlarged and shrunken ellipses(steps 95, 159) are retained for as possible nodes for use in pathgeneration.

Reference is now made to FIG. 11, which is a flow chart detailinggeneration of a path according to step 141 (FIG. 7), in accordance withan embodiment of the invention. Nodes are identified by index values,which are pointers to data objects describing the mesh. Otherwise, theseindex values have no physical significance. At initial step 163 A randomnumber (Uniform[0; 2π]) is generated, and used as the index along thesource's surface. The corresponding node of the mesh file becomes theorigin of the path.

Next, at step 165 the blocking value of the node selected in initialstep 163 is assigned as the current blocking value of the path.

Next, at step 167 a step of the path is generated. The step leads to arandomly selected neighboring node. A node and a neighboring node aredirectly connected. The distance therebetween in abstract space is “1”.

Next, at decision step 169, it is determined if the blocking value ofthe neighboring node selected in step 167 is less than the currentblocking value. If the determination at decision step 169 isaffirmative, then control proceeds to step 171. The current blockingvalue is reset to the blocking value of the neighboring node.

After performing step 171 or if the determination at decision step 169is negative, then at decision step 173, it is determined if theneighboring node chosen in step 167 is a destination node.

If the determination at decision step 173 is negative, then controlreturns to step 167 to continue generation of the path.

If the determination at decision step 173 is affirmative, then at finalstep 175 the current blocking value is reported as the blocking value ofthe path.

Combined Variant.

Some aspects of the no-map variant can be used to improve the efficiencyof computing the map file variant. Locations on the mesh that are farfrom the original ablation sites can be projected to the simulationplane and the nearest node can be selected according to the2-dimensional Euler distances.

Second Embodiment

In this embodiment paths between the source and the destination are notcalculated. Rather the gap is found from geometrical considerations. Atree graph is built so that paths between all sites have segments ofminimal length.

Reference is now made to FIG. 12, which is an intermediate graph that isuseful for constructing a tree graph of ablation sites in accordancewith an embodiment of the invention. Nodes of the tree graph areidentified by numbers, which are indices to data records of theirassociated ablation sites. A pair of ablation sites comprises a nodeconnected to its nearest node by an edge. One pair 177 is delineated bya broken circle. A cluster 179 of nodes is outlined by a broken circle.

Reference is now made to FIG. 13, which is a flow chart of a method ofpath generation in accordance with an embodiment of the invention. Themethod finds a path necessary for isolating the source from thedestination that has the smallest blocking value. The largest segment ofthe path is reported as the gap.

At initial step 181 a sample mean is identified, i.e., a mean of a setof position vectors of all the ablation sites, and the points arecentered about the mean by subtracting the mean from each of the othervectors.

Next, at step 183 for each point, a pair is defined as a graph edge tothe nearest other point. Two points may be found to be connectedindirectly. All duplicate edges are removed at step 185. Implementationsof initial step 181 and step 183 are detailed in the Mathematica code ofListing 1. Other listings herein are also expressed in Mathematica code.

Listing 1

-   -   cent=Mean[dataSet];    -   centeredDataSet=#−cent &/@ dataSet;    -   NearestF=Nearest[centeredDataSet→Automatic];    -   firstgrdat=Union[UndirectedEdge @@ Sort@NearestF[#, 2] &/@        centeredDataSet];

Reference is now made to FIG. 14, which is a simplified graphillustrating step 185 (FIG. 13) in accordance with an embodiment of theinvention. A point 187 is a nearest neighbor of point 189 (measured bythe Euler 3-dimensional distance). The points 187, 189 are connected byedge 191. In like manner point 189 and point 193 form a pair connectedby edge 195. Yet another pair comprises points 187, 193 connected byedge 197. However, edge 197 is redundant and is therefore deleted, asshown on the right side of the figure.

Reverting to FIG. 13, in the following steps a graph is constructed fromall the edges remaining after performing step 185. Clusters are definedas connected components in the graph, for example, cluster 179 (FIG.12).

At step 199 the points in each cluster are sorted by index. It will berecalled that the index is an arbitrary reference to a data object. Whenstep 199 is complete the first point in the sorted cluster has thesmallest index in that cluster.

Then at step 201 a list of clusters is sorted by the index of the firstpoint within the clusters, so that the order of the clusters changes, asshown in Listing 2

Listing 2

-   -   firstcon=SortBy[Sort/@ ConnectedComponents[firstgr], First];

Next, at step 203 a sorted list of the first positions of each clusteris derived from the sorted list of clusters that was prepared in step201 to identify each point with the identifier of the first point in itscluster, as shown in Listing 3.

Listing 3

-   -   firstList=Table[Position[firstcon, i, 2] [[1, 1]], {i,        Sort@Flatten@firstcon}];

In step 205, all possible pairs of points are mapped and sortedaccording to the distances between members of the pairs to form a sortedlist of all possible edges. Duplicates are then removed.

Step 207 comprises connecting the clusters by iteration over the sortedpairs. If indices of a pair relate to more than one cluster, the pair isretained and the two clusters are coalesced. The process is aborted whenall points are in the same cluster.

Reference is now made to FIG. 15, which is a typical graph resultingfrom the performance of step 207 (FIG. 13) in accordance with anembodiment of the invention.

Next, at step 209 the graph of FIG. 15 is enlarged by forming a unionwith the intermediate graph of FIG. 12. The procedure is detailed inListing 4.

Listing 4

-   -   pathdat=Union[firstgrdat, restgraphdat]    -   GraphUnion[firstgr, restgraph]

Reference is now made to FIG. 16, which is a typical tree graphresulting from the performance of step 209 in accordance with anembodiment of the invention. The tree graph defines a path constructedof the shortest segments for each pair of points.

Reference is now made to FIG. 17, which is a 3-dimensional presentationof the points corresponding of the tree graph of FIG. 16, in accordancewith an embodiment of the invention. FIG. 16 and FIG. 17 represent apath constructed of the shortest segments connecting each pair ofpoints.

Reverting to FIG. 13, at step 211 edges of the tree graph produced instep 209 are removed from the sorted list that was created in step 205.At this step multiple gaps in multiple isolations of signals may bereported.

After performing step 211 a gap through the ablated sites may optionallybe identified based on a new source. When this option is omitted, asindicated by a broken line, control proceeds to final step 213, which isdescribed below. Otherwise, the operator at step 215 selects a point,for example, by a mouse click on the display. Other methods may be usedby the operator or chosen automatically to select one or more points ofsources that he wishes to isolate.

Next, at step 217 the 3-dimensional intercepts of the mouse position areidentified as a pair of vectors that define a line segment. This may beunderstood by the mouse click defining a ray extending from the mousepointer into the screen. A virtual 3-dimensional box containing allrelevant points, intersects with the ray twice. Each point ofintersection has 3-dimensional coordinates. All the ablation site pointsare centered about the center of the line segment connecting theintersections.

Next, at step 219 a rotation operation is conducted such that the x-axisaligns with the direction of the line segment defined by the mouse clickin step 217. The points are then projected onto the x=0 plane. Becausethe points were centered about the mouse position, the coordinate originis a convenient point of reference for the rotation.

The next steps describe an iteration over the sorted list of edges, inwhich the shortest segment that complies with a predetermined gapcriteria, e.g., a winding number of ±1 is retained. At step 221 for eachedge a graph of the edges is created. This graph is the union of thetree graph with an additional edge. Adding an edge to a tree graph inthis manner produces a loop. Thus, this graph has only one loop sincethe tree graph has no loops and has all of its points connected.

Next, at step 223 a sub-graph of all of the graph vertices that are corecomponents of order 2 is selected. This sub-graph is a pure loop and hasno weakly connected elements. In graph theory, a k-degenerate graph isan undirected graph in which every subgraph has a vertex of at mostdegree k: that is, some vertex in the subgraph touches k or fewer of thesubgraph's edge. Degeneracy is also known as the k-core number. For thepurpose of this disclosure a sub-graph having weakly connected elementshas a k-value less than 2.

Next, at decision step 225, it is determined if the loop of the currentsub-graph includes, i.e., encompasses the origin. If a 2-dimensionalpoint is within a 2-dimensional polygon, the sum of the interior anglesof the polygon sides should be exactly 360°. One way of determining ifthe loop includes the origin is to sum the differences of thearctangents of the points in each edge of the loop graph, correcting therange appropriately in order to deal with discontinuities. Since at x<0,y=0 the arctangent jumps from +180° to −180°, the angle coverage of eachsegment should be corrected to the (−180°, +180°) range. If the finalsum is ±360°, the loop includes the origin.

If the determination at decision step 225 is negative, then controlreturns to step 223 to continue the iteration by generating a newsubgraph from the next edge (in order of length).

If the determination at decision step 225 is affirmative, then it isconcluded that the gap has been found. The gap is reported at final step213. The length of the gap is the Euler distance between the3-dimensional vertices on either side of the gap edge. Optionally, bycalculating the lengths of the all edges of the loop graph, more gaps,e.g., any number of smaller gaps can be reported. For the convenience ofthe operator, by selecting a high contrast color scheme and an objectivegap size range, the gaps can be colored according to their lengths.

Reference is now made to FIG. 18, which is an exemplary loop graph inabstract space that is evaluated step 221 in accordance with anembodiment of the invention.

Reference is now made to FIG. 19, which is a composite screen displaythat was produced in accordance with an embodiment of the invention. A3-dimensional presentation of ablation points is seen in pane 227.Points projected on a simulation plane are shown in pane 229. A key 231indicating gap sizes is shown in the upper right portion of the display.A gap 233 measuring 7.5 mm is shown in the pane 227.

Reference is now made to FIG. 20, which is a screen display illustratingmultiple gaps found in a collection of ablation points when theprocedure beginning at step 215 is performed and wherein all reasonablesources are found automatically in accordance with an embodiment of theinvention. Three gaps were discovered, which are the largest among thegaps discovered by the procedure of FIG. 7 and reported at final step145. Their sizes are labeled on the figure.

Additional Considerations.

Once the sizes of the lesions of the ablation sites are calculated by aformula, the site radii can be removed from the length of each edgelength before sorting. The result will be the largest gap betweenestimated lesions instead of the largest gap between site centers.

Finding a gap in a line: Once a beginning and end sites are determined,the shortest path can be found using graph theory. The path segments canbe sorted and colored objectively as for gap in a loop.

Excluding points: The entire procedure can be performed on a subset ofthe ablation sites.

Automated gap finding: Given a set of input parameters, the algorithmcan search for loops and gaps automatically, as shown in position sensor21.

Instead of testing if a loop includes the origin in decision step 225(FIG. 13), the gap criteria for automated gap finding can include:

The minimum number of sites in a loop (e.g. 8).

The minimum size of the loop (e.g. 9 mm, determined by the mediandistance of the points from the loop center).

The maximum gap opening (e.g. 45°).

The maximum gap size (e.g. 40 mm).

Proposition

The following proof forms a logical basis for the processes describedabove: Given a set of discrete closed curves on a 2D surface and a pointsource, the isolation is the curve with unit winding number that isconstructed of segments with the smallest segment lengths.

Proof

1. Let us assume that we have generated all of the possible paths fromthe source to the destination (named the path set).

2. Let us assume further that we have a fine set of segment thatconstruct all possible discrete contours with unit winding number aboutthe source (named the segment set and the contour set, respectively).

3. Each path in the path set intersects with all of the contours in thecontour set.

4. Assuming that resistance to current flow is inverse to the size of acontour gap, a path that intersects the contour having the smallest gapexperiences the greatest resistance at that gap.

5. Let us collect these segments and name the set the suspected segmentset.

6. The least hindered paths are the paths that intersect the segmentfrom the suspected set with the largest segment length. Therefore, thissegment has the largest gap in the isolation, and will be part of theisolation.

7. Removing all contours that do not include this segment from thecontour set (so that only segments that are part of the remainingcontours are left in the segment set and the suspected set), the nextlargest segment in the suspected set is the next in order cause ofcurrent leak, and therefore is also part of the isolation.

8. Repeating this process leaves us with only one contour, which is theone with the segments with the smallest segment length by order, andthis contour is the isolation.

It will be appreciated by persons skilled in the art that the presentinvention is not limited to what has been particularly shown anddescribed hereinabove. Rather, the scope of the present inventionincludes both combinations and sub-combinations of the various featuresdescribed hereinabove, as well as variations and modifications thereofthat are not in the prior art, which would occur to persons skilled inthe art upon reading the foregoing description.

The invention claimed is:
 1. A method for determining a gap in anablated region of tissue, comprising the steps of: ablating a pluralityof sites in a heart of a living subject, the sites having respectivelocations in a 3-dimensional coordinate system; projecting the locationsof the sites onto a simulation plane; defining a source and adestination; projecting the source and the destination onto thesimulation plane, wherein the projected locations of the sites liebetween the projected source and the projected destination on thesimulation plane; randomly generating a set of 2-dimensional paths thatcorrespond to 3-dimensional connections between pairs of the projectedlocations of the sites on the simulation plane extending from theprojected source to the projected destination, each path having passagesbetween the projected locations of sites in each pair of projectedlocations of sites, the passages having respective sizes; and for eachof the 2-dimensional paths determining a minimum size of the passagesthereof, wherein reporting a gap comprises reporting the largest minimumsize of the 2-dimensional paths.
 2. The method according to claim 1,wherein the projected locations of the sites lie on an ellipse of bestfit, wherein a portion of the projected locations of the sites lieoutside the ellipse, further comprising enlarging the ellipse to includeall of the projected locations of the sites.
 3. The method according toclaim 1, further comprising the steps of: modeling a portion of theheart as a triangular mesh comprising mesh nodes and ablation points,respective ablation points having a nearest mesh node; from the meshnodes preparing a grid graph having graph nodes that are connected byundirected edges; representing the ablation points on the grid graph ascorresponding graph nodes of the nearest mesh node thereof; and usingthe corresponding graph nodes as the projected locations of the sites inthe step of generating 2-dimensional paths.
 4. A method for determininga gap in an ablated region of tissue, comprising the steps of: ablatinga plurality of sites in a heart of a living subject, the sites havingrespective locations in a 3-dimensional coordinate system; building atree graph from all of the locations of the sites, the tree graph havingedges and defining a path constructed of shortest segments between pairsof the sites; selecting a source, wherein the tree graph has a loop thatwinds about the source, the loop describing a gap between two of theablation sites; and reporting a shortest edge in the tree graph that canclose the gap as a gap size.
 5. The method according to claim 4, furthercomprising selecting additional sources and iterating the step ofbuilding a tree graph using the additional sources.